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# What is open loop gain of TL431

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#### cupoftea

Hi,
In the attached AN-57, do you know what is the "K(TL431)" value? (page 14).....the open loop gain of the TL431.
We are trying to stabilise a 20W TOP256GN Flyback, and need to know the K(TL431) so we can calculate the feedback bodes.

TL431

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Hi,

I reommend to have a look in the datasheet of the TL431 from other manufacturers e.g. [1] & [2] as they do provide gain information.

Further, there is plenty information on the web supporting the design of switching power supply using the TL431 e.g. [3], [4] & [5]

[2] https://www.st.com/en/power-management/tl431.html
[3] https://www.onsemi.com/pub/Collateral/TND381-D.PDF
[4] https://www.plexim.com/files/plecs_tl431.pdf
[5] https://www.ti.com/lit/an/sluaa66/sluaa66.pdf?ts=1688932033825

BR

Thanks, and i assume that by the "open loop gain of the TL431", they mean Z(FB)/Z(in) of the TL431 circuit in Fig 5, page 4 of the AN-57 Application note.....
where:
Z(FB) = 1/(2.pi.f.CF1)
and
Z(IN) = RF2
?
(The AN-57 App Note is attached in the Top Post here)

Thanks, and i assume that by the "open loop gain of the TL431", they mean Z(FB)/Z(in) of the TL431 circuit in Fig 5
No. K(TL431) is obviously the internal TL431 gain, as documented in datasheets. It's a voltage transfer function.

Below is from the TI TL431 data sheet:
It looks to have about 55dB of low frequency gain, with a gain-bandwidth of about 1.8MHz.

cupoftea

### cupoftea

Points: 2
Thanks, so we will be concerned with the gain at around the xover freq, which is around 1kHz, so thats 55dB of gain.
So 20.log(10) vout/vin = 55dB.

As such, v(out)/v(in) = 10^(55/20) = 562

....as you know, Its unusual to see this in an error amplifier transfer function, because usually they just assume the opamp gain is infinite, and do the z(fb)/z(in) calculation for the gain of the error amp.

No. K(TL431) is obviously the internal TL431 gain, as documented in datasheets. It's a voltage transfer function.
Thanks, thats interesting, especially because Dr Basso, in his book, does not include the "open loop gain of the TL431", in his equation for this transfer function, which is shown here attached on page 467. (equation 8.35)
Basso's book is "Designing control loops for...........".

As we know, the Power Integrations transfer function for this same thing is in AN-57, and is equation 25, which includes equation 23 (equation 23 includes the K(TL431) parameter).

Interesting that Basso does not include K(TL431), but power integrations do....they are both referring to the same thing.
--- Updated ---

(Sorry , forgot to say, AN-57 is linked in the top post)

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we will be concerned with the gain at around the xover freq, which is around 1kHz
Unfortunately it doesn't show the phase-shift, but I think it would be near zero at 1kHz, since the gain looks fairly flat around that frequency.

The datasheet from ST linked in post #2 is showing the phase ....

BR

A voltage gain of 562 implies for a 1mV change at the ref pin, you get 562mV at the kathode DC- 1kHz

While this is not outstanding - it is generally good enough for a run of the mill power supply - esp as the current drawn thru an opto coupler would increase fairly markedly for an extra 0.562V applied

so the voltage to current gain would be higher . . .

The difference between Bassa and AN57 is that the former treats TL431 as ideal (infinite gain). In practice, that's appropriate for transfer function calculation, finite DC gain matters however for statical regulation performance, it can be estimated separately without looking at H(s).

Thanks, in AN-57 (linked in the top post), on page 5, equation 4, they give an equation for the "KC" value......this equation, they say, relies on the assumption that "RF3 = 1".
RF3 is the resistor in series with the feedback opto.....seen in page 4 Fig 5.

It sounds totally wrong to assume that this is 1 Ohm.

But since the "KC" value is needed to calculate the G(CONTROLLER)(s), on page 14, then it looks like there is now no hope of calculating the open loop feedback transfer function for TOPswitch flyback.

May anyone throw any light on this as all?

I think you don't read AN-57 thoroughly. There are no unknown parameters.

Thanks, yes i know, but why should we consider "RF3=1"? (as on page 5)
1 Ohm is too low.

Also, why should we assume Q=0.15?.(as on page 6)...it seems to assume that we have a high sec coil resistance. We in fact dont.

Shouldnt we calc Q as Z/R of the series LC circuit comprising L(sec) and C(out)?
--- Updated ---

Also, on page 7 of AN57, there is an extra resistor called "R".
So therefore, you assume that in the equation of equation 3, page 5...you assume that "RF2" should actually be "RF2 + R"?
--- Updated ---

....although i mean RF2 from the schem of page 4...its a little confusing, as they have the same schem with different designators

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Hi,
AN-57 is attached to top post.
Top RHS of page 6 of AN57 says the resonant frequency between c(out) of the flyback, and the "effective L(sec)" should be <500Hz.
This stipuation has never before occurred for any flyback converter, in any text or book.
Do you know what this is abou?....And why it should be so?
We are using a Rubycon YXF capacitor of 35v, 1mF. Our L(sec) is 54.5uH...And D = 0.55 (at 90vac) and NS/NP = 19/84.....so our resonant frequency is 306Hz...therefore we violate the rule.....

Is it something to do with the voltage mode control.....?...Topswitch is voltage mode controlled from 100% of load to 55% of load.

Hi,
(This is from AN-57, linked in the top post above.)
Voltage mode offline flybacks have hard limit to amount of output capacitance.

I am sure you will have read the differences between voltage mode and current mode Flyback converters…eg…

https://www.ti.com/lit/an/slua119/slua119.pdf?ts=1689339883959&ref_url=https%3A%2F%2Fwww.ti.com%2Fproduct%2FUC1842

But few will have realised that a voltage mode flyback is not allowed as much output capacitance as a current mode flyback. No matter how the compensation components are adjusted, with voltage mode, you have a hard limit to the amount of output capacitance that you can have…..the limit is given on page 4 (bottom left of page) of AN-57 by Power Integrations.

As can be seen, you must calculate the “effective secondary inductance” of the flyback (LE), then the resonant frequency of this with the output capacitance, must be >500Hz….thence you have the limit to the output capacitance.

But now it is known. Do you agree with it?

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